Problem: What is the greatest common factor of $44c^{5}$, $22c^{3}$, and $11c^4$ ?
Let's factor each monomial to its prime factors: $\begin{aligned} 44c^{5}&=(11)(2)(2)(c)(c)(c)(c)(c) \\\\ 22c^{3}&=(11)(2)(c)(c)(c) \\\\ 11c^{4}&=(11)(c)(c)(c)(c) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ {11}$ and three factors of $ c$ : $\begin{aligned} 44c^{5}&=( {11})(2)(2)( c)( c)( c)(c)(c) \\\\ 22c^{3}&=( {11})(2)( c)( c)( c) \\\\ 11c^{4}&=( {11})( c)( c)( c)(c) \end{aligned}$ This is the greatest common factor: $( {11})( c)( c)( c)=11c^3$